Chapter 8, Problem 9PT

To determine

The width of the given rectangle.

Answer to Problem 9PT

The correct option is C.

Explanation of Solution

Given:

The rectangle is given as:

  

The expression for the area of the rectangle is given as:

  $2x^2-x-15$

The options are given as:

  $\begin{array}{l}Ax-5\\ Bx+3\\ Cx-3\\ D2x-3\end{array}$

Here 2x+5 is the length of the rectangle.

The area of the rectangle is the product of the length and width.

Factorizing the area of the rectangle:

  $\begin{array}{l}2x^2-x-15\\ =2x^2-6x+5x-15\\ =2x9x-3+5\left(x-3\right)\\ =\left(x-3\right)\left(2x+5\right)\end{array}$

From the above factors, the width of the rectangle is $\left(x-3\right)$ .

Therefore, the correct option is C.